Stability Guarantees For Neural Network Controlled Systems.
As neural networks become popular in control tasks, safety and robustness of neural networks and neural network controlled systems has been actively discussed [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. Closely related to this work are recent papers on robustness analysis of memory-less neural networks controlled systems based on robust control ideas. [12]}, [13]}, [14]}, [15]} conduct stability analysis of neural network controlled linear and nonlinear systems and propose verification methods by characterizing activation functions using quadratic constraints. [16]} adds additional projection layer on the controller to ensure stability for fully observed systems. [17]} studies the stability of RNN itself when fitted to data but does not consider any plant to control by such RNN. The most related works are those that study dynamic neural network controllers. [18]}, [19]} adapt RNN controllers through RL techniques to obtain stability guarantees. However, in these works, the reward function is assumed to be known, and conservative updates of controller parameters projected to a box neighborhood of the previous iterate are applied due to the non-convexity in their conditions. In contrast, our work enables much larger and more efficient updates thanks to jointly convex conditions derived through a novel sequential convexification and loop transformation
approach unseen in these works.
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